Self-inductance ($\Lambda =LI,{\mathcal{E}}_{\mathrm{ind}}=-L\dot{I}$)

For a circuit whose flux linkage $\Lambda$ is proportional to its current, the self-inductance is the coefficient $L$ in $\Lambda =LI$. Faraday's law gives the induced electromotive force $-L\dot{I}$ when $L$ is constant. In series with a resistance $R$ and a constant applied electromotive force, the current obeys $L\dot{I}+RI={\mathcal{E}}_0$, with time constant $L/R$.